# Blank Place Value Charts Notes on Use of the LLP Option Pricing Model for

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```					Notes on Use of the LLP Option Pricing Model for Puts

The LLP option pricing model is based on a least-squares regression equation
that uses the natural logarithms of (asset price/strike price) to predict the
natural logarithms of (option price/strike price). The price curve generated in
logarithms is a parabola whose values are converted into arithmetic terms
by computing the antilog values.

The accuracy of LLP option price curves in matching actual market prices is
illustrated by the chart on the following worksheet. For this sample of sixteen
put options, the predictive price curve almost completely obscures the original
market prices.

Currently, the LLP pricing spreadsheet is arranged to contain up to twenty
combinations of asset price, strike price and call option price. The minimum
number needed to compute a price curve is three combinations

Price data should be entered in columns A, B and C. On the worksheet,
data to be entered is shown in black numerals, calculation formula cells in
blue, and output formula cells in red. The formula cells have not been
protected against accidental changes by the user, thus it is recommended
that file copies be made of the LLP and Black/Scholes worksheets.

The least squares regression computations take place starting at Column J,
and ultimately produce the A, B and C coefficients of the parabolic equation.
Values generated by the model, in addition to the predicted option prices,
include the intrinsic values (for puts, equal to the strike price less the asset
price at each point), hedge ratio (the slope of the curve at each point), and
upper and lower breakeven prices for each delta-neutral hedge -- the points at
which the slope line (not shown) intersects the intrinsic value and the horizontal axis.

One important note in using the LLP model is to recall that the price curve
in natural logs is a parabola. This means that when the predicted curve is carried
outside a "relevant" range there are unusual price results -- such as the
price curve intersecting and passing through the intrinsic value line. The charts
on the LLP worksheets show how well the model describes actual market
prices when the calculations fall within the range bounded by the horizontal
axis (where the option price is equal to zero) and the intrinsic value line.

If the numeral 2 is entered in cell H3, then the ratio (between zero and 1.0)
entered in cell H2 becomes the input hedge ratio for every point on the
price curve in place of the delta values originally computed. A new ratio
may be inserted in cell H2 in order to reflect the bullish or bearish feelings
of the user regarding the underlying asset price. A larger ratio makes the
option's price change at a greater rate per one unit change in the underlying
price, and means that the underlying asset may be hedged with fewer
options. The new ratio entered in cell H2 affects options at each strike price,
although you may be interested in changing a specific one.

The upper and lower breakeven prices at expiration will change with the
new ratio entered. If cell H3 is left blank or contains anything other than the
numeral 2 the ratio in cell H2 will not affect the calculated option prices.

Source of data for futures and option prices: Chicago Mercantile Exchange.
new ratio =                      0.50
number =                     16                                                                                if H3 = 2                           0

Sept 08 Euro FX Futures Put Options
April 14, 2008
P                S
Put          Predicted
Asset            Strike          Option            Option         Intrinsic          Hedge             Lower            Upper                                                 Predicted Precicted
Price             Price            Price            Price            Value            Ratio              B-E              B-E                                                   LN W/E             W/E              S/E               W/E             LN S/E           LN W/E           SUM1                SUM2              SUM3              SUM4               SUM5                SUM6              SUM7                S8                S9                   T1            D1                CP
---------------- ----------------- ---------------- ---------------- ---------------- ----------------- ---------------- -----------------                                       ---------------- ---------------- ----------------- ----------------- ---------------- ---------------- ----------------    ----------------- ----------------- ----------------   ----------------                                  -------------------------
----------------- -----------------                  ----------------- ----------------- ---------------- -----------------
1.5679              1.600          0.0585           0.0586           0.0321          -0.6178            1.4732           1.6626                                            -3.3074576 0.0366091 0.9799375 0.0365625 -0.0202665 -3.3087322 0.0670564                                                    -0.0202665 -3.3087322 0.0004107                        -8.324E-06           -0.001359 1.687E-07 0.0048013 8.463E-05                                   -0.087716645 0.0023475 -29.777627
1.5679              1.595          0.0554           0.0554           0.0271          -0.5912            1.4742           1.6616                                                -3.35951 0.0347523 0.9830094 0.0347335 -0.0171366 -3.3600494 0.0575798                                                  -0.0171366 -3.3600494 0.0002937                        -5.032E-06          -0.0009867 8.624E-08
1.5679              1.585          0.0496           0.0495           0.0171          -0.5401            1.4761           1.6597                                            -3.4658702 0.0312458 0.9892114 0.0312934 -0.0108473 -3.4643489 0.0375787                                                    -0.0108473 -3.4643489 0.0001177                        -1.276E-06          -0.0004076 1.384E-08                     T2                T3                   C2            D2                BP
1.5679              1.570          0.0417           0.0416           0.0021          -0.4685            1.4789           1.6569                                            -3.6311486 0.0264857 0.9986624 0.0265605 -0.0013385 -3.6283298 0.0048564                                                    -0.0013385 -3.6283298 1.792E-06                        -2.398E-09             -6.5E-06                                         ----------------- -----------------
3.21E-12 -------------------------                                 ----------------- -----------------
1.5679              1.565          0.0392           0.0392          -0.0029          -0.4460            1.4800           1.6558                                            -3.6877987          0.025027         1.001853 0.0250479 0.0018513 -3.6869644 -0.0068258                                      0.0018513 -3.6869644 3.427E-06                         6.345E-09          -1.264E-05 1.175E-11 2.881E-06 -0.0015875                                   0.004801294 -7.883E-05 -17.744513
1.5679              1.560          0.0369           0.0369                           -0.4243            1.4809           1.6549                                            -3.7452389           0.02363 1.0050641 0.0236538 0.0050513 -3.7442295 -0.0189133                                             0.0050513 -3.7442295 2.552E-05                         1.289E-07          -9.554E-05 6.511E-10
1.5679              1.555          0.0346           0.0347                           -0.4032            1.4821           1.6537                                            -3.8034764 0.0222931 1.0082958 0.0222508 0.0082616 -3.8053771 -0.0314385                                                     0.0082616 -3.8053771 6.825E-05                         5.639E-07          -0.0002597 4.659E-09                     DV                C1                   C3                              AP
1.5679              1.550          0.0325           0.0326                           -0.3829            1.4830           1.6528                                            -3.8625181          0.021015 1.0115484 0.0209677 0.0114822 -3.8647701 -0.0443761                                             0.0114822 -3.8647701 0.0001318                         1.514E-06          -0.0005095 1.738E-08 -------------------------      ----------------- -----------------                   ----------------
1.5679              1.545          0.0305           0.0306                           -0.3632            1.4839           1.6519                                            -3.9223713 0.0197941                 1.014822 0.0197411 0.0147132 -3.9250525 -0.0577502                                      0.0147132 -3.9250525 0.0002165                         3.185E-06          -0.0008497 4.686E-08 56.733931 -0.0900641                                   0.000163462                   -3.6548459
1.5679              1.540          0.0287           0.0287                           -0.3442            1.4845           1.6513                                            -3.9830433 0.0186289 1.0181169 0.0186364 0.0179547 -3.9826406 -0.0715072                                                     0.0179547 -3.9826406 0.0003224                         5.788E-06          -0.0012839 1.039E-07
1.5679              1.535          0.0269           0.0269                           -0.3260            1.4854           1.6504                                            -4.0445414 0.0175177 1.0214332 0.0175244 0.0212068 -4.0441594 -0.0857635                                                     0.0212068 -4.0441594 0.0004497                         9.537E-06          -0.0018188 2.023E-07
1.5679              1.530          0.0252           0.0252                           -0.3084            1.4862           1.6496                                              -4.106873 0.0164592 1.0247712 0.0164706 0.0244694                                      -4.106179 -0.1004758                0.0244694          -4.106179 0.0005988                 1.465E-05          -0.0024586 3.585E-07
1.5679              1.525          0.0236           0.0236                           -0.2915            1.4869           1.6489                                            -4.1700458 0.0154515 1.0281311 0.0154754 0.0277427                                       -4.168503 -0.1156457                0.0277427          -4.168503 0.0007697                 2.135E-05          -0.0032083 5.924E-07
1.5679              1.520          0.0220           0.0220                           -0.2753            1.4880           1.6478                                            -4.2340673 0.0144933 1.0315132 0.0144737 0.0310268 -4.2354232 -0.1314117                                                     0.0310268 -4.2354232 0.0009627                         2.987E-05          -0.0040773 9.267E-07
1.5679              1.515          0.0206           0.0206                           -0.2597            1.4886           1.6472                                            -4.2989453 0.0135829 1.0349175 0.0135974 0.0343217 -4.2978796 -0.1475106                                                     0.0343217 -4.2978796                  0.001178         4.043E-05          -0.0050628 1.388E-06
1.5679              1.510          0.0192           0.0192                           -0.2448            1.4895           1.6463                                            -4.3646874 0.0127186 1.0383444 0.0127152 0.0376275 -4.3649547 -0.1642423                                                     0.0376275 -4.3649547 0.0014158                         5.327E-05             -0.00618 2.005E-06
0.0000                         #DIV/0!           #DIV/0!          #DIV/0!                                              -3.6548459 0.0258655                           0                 0                 0                0                0                   0                 0                 0                  0                   0                 0
0.0000                         #DIV/0!           #DIV/0!          #DIV/0!                                              -3.6548459 0.0258655                           0                 0                 0                0                0                   0                 0                 0                  0                   0                 0
0.0000                         #DIV/0!           #DIV/0!          #DIV/0!                                              -3.6548459 0.0258655                           0                 0                 0                0                0                   0                 0                 0                  0                   0                 0
0.0000                         #DIV/0!           #DIV/0!          #DIV/0!                                              -3.6548459 0.0258655                           0                 0                 0                0                0                   0                 0                 0                  0                   0                 0
---------------- ----------------- ---------------- -----------------   ---------------- ---------------- ----------------
-0.8087893 0.1861205 -61.987593 0.0069663                                0.0001657 -0.0285767 5.914E-06
Predicted Option Price Curve
----------------------------------------------
A = -3.6548459
B = -17.744513
Sept 08 Euro FX Futures Put Options
C = -29.777627

Time Premium where P = S
0.0700

2.59%
0.0600

At the strike price, height of option                                      0.0500
price curve as percent of the
Option Price

strike price. Indicator of relative                                        0.0400
volatility and value of remaining
time to expiration.                                                        0.0300

The jump in strike prices causes                                           0.0200
a jagged progression of prices
instead of a smooth curve on the                                           0.0100
chart.
0.0000
1.600
1.595
1.585
1.570
1.565
1.560
1.555
1.550
1.545
1.540
1.535
1.530
1.525
1.520
1.515
1.510

-0.0100
Strike Price

Put Option Market Prices                             LLP Predicted Prices                                 Intrinsic Value

Note: On this chart the predicted prices overlay the put market prices due to high
correlation between the two series.

Some of the intrinsic values in Column E were deleted in order to improve the chart
shown above. If needed they can be recalculated by copying the formula in cell E16.

```
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Description: Blank Place Value Charts document sample